Showing expense ratio of a fund in real dollar terms

Question

I'm a mostly-passive investor with some 401ks spread around the past few jobs I've had. I knew I should probably do "something" with them (the only option I had considered was rolling into my current 401k).

As a longtime lurker on this site, I knew about IRAs, but for some reason I never made the two logical leaps required to get where I am today: 1) you choose your investments in an IRA, and 2) you can roll over old 401k's into them.

Today, I finally made those connections. Now I'm curious how to compare the performance of my 401k versus the assets I'd choose to invest in, except in real dollars.

The growth side seems pretty straightforward: if you have $100,000 in a vehicle that grows 10% year over year, you'll end your first year with $110,000.

Here's my question: I feel like the expense side is pretty clear as well, but I haven't been able to find anybody showing the simple math, so I'm not certain that this is how best to conceptualize it. Say I have $100,000 in a fund with a .5% expense ratio. That means my portion of the fund will lose $500 in value -- that is, it's the same math as the growth side (get .5% of the value and subtract instead of add it to the total)?

Combining the two, a $100,000 fund with 10% growth and a .5% expense ratio will end the year with $109,500 -- or 9.5% growth?

(This part is for my benefit. The best way to get me to focus on small changes in investing is to show how dramatic they become over time!) Extrapolating over 10 years, the fund without the expense ratio and no additional contributions will finish up at just shy of $260,000 and with the expense ratio will end at $247,000 for a difference of $13,000. Over 30 years, it looks like the delta will be $200,000.

Does my math add up? I'm always impressed with compound interest every time I calculate it, and if my math here is correct, today will be no exception!

(ps: in case anybody is trying to look deeper into the numbers, I deliberately used round numbers to simplify the math)

Answer 1

As Ben Voigt's comment points out, the stated growth rate of your mutual fund investment is after the expense ratio has been deducted. Thus, in broad terms, if the fund tells you that your investment increased in value by 10% and you know that the expense ratio is 0.5%, the actual growth of the underlying investment was 10.5% but some of the assets were "sold" to pay the expenses leaving a net growth of 10%. In practice, the fund does not have all its assets (i.e. every penny) invested in stocks or bonds etc; there is a cash account into which new incoming investment money is deposited before it is invested and from which redemptions of shares are paid to the investors, and the fund's operating expenses (the stuff making up the expense ratio) are paid on a daily basis. Thus, often no assets are physically sold to pay the expense ratio -- it is usually just taken out of this "petty cash" account -- with 0.5%/365th of the assets being removed each day as the management fee for the account.

So, "Combining the two, a $100,000 fund with 10% growth and a .5% expense ratio will end the year with $109,500 -- or 9.5% growth?" is not quite right. You will end up with $110,000 for a 10% growth rate; the expense ratio has already been accounted for in the announcement of the growth rate.